file copy 4'9 - world bank

14 X12LT H E WORLD BANK ECONOMIC REVIEW, VOL. 4, NO. 2: 2 0 9 - 2 3 3

FILE COPY 4'9Voluntary Export Restraints and Resource

Allocation in Exporting Countries

Jaime de Melo and L. Alan Winters

This article analyzes the resource implications of voluntary export restraints (vERS)

for exporting countries. A simple analytical method is used to demonstrate that, byreducing the marginal revenue of its factors of production, a VER causes an industryin the exporting country to contract, and that the efficiency losses from a VER dependon the ease with which sales can be diverted from the restricted toward the unrestrictedmarkets. The method is applied to test the effects of the U.S. Orderly MarketingAgreement (oMA) for producers of leather footwear in the Republic of Korea duringthe period 1977-81. We estimate that the marginal revenue product of factorsemployed in leather footwear declined by as much as 9 percent because of the OMA,

an estimate that is corroborated by inspection of time series on output, employment,and wages of the Korean footwear sector. This implies that there was pressure on theKorean footwear industry to contract as a result of the OMA.

Most previous investigators of the effects of voluntary export restraints havebeen concerned with the welfare costs of such restraints to consumers in im-porting countries. Examples of previous studies include: estimates of qualityadjusted welfare costs of VERS on automobiles (Feenstra 1984; Dinopoulos andKreinin 1988); the claim that, for commodities with little product differentia-tion and low start-up costs (for example, footwear and textiles), VERS areineffective (Baldwin 1982; Bhagwati 1986); and simulations which show thatterms of trade effects are likely to reduce substantially the costs of (gains from)VERS to importing (exporting) countries (Tarr 1987; Trela and Whalley 1988).None of these studies-even those which look into the implications of VERS forexporters-contain investigations into the effects of VERS on resource allocationin exporting countries. This article fills the gap.

For the sake of simplicity, we analyze the effects of a VER in two steps. First,

Jaime de Melo is an economist at the World Bank and an associate of the Centre for Economic PolicyResearch, London. L. Alan Winters is a professor of economics at the University of Birmingham andan associate of the Centre for Economic Policy Research. The authors thank three referees, WendyTakacs, Paul Brenton, and Taeho Bark, participants at the Centro Interuniversitario di Studi Teoricf perla Politica Economica-Centre for Economic Policy Research Conference in Venice, May 1988 and atthe European Research Workshop in International Trade in Bergen in July 1989 for helpful commentson an earlier draft. They also thank Maria Ameal and Alexander Pfaff for logistical support.

© 1990 The International Bank for Reconstruction and Development / THE WORLD BANK.

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210 THE WORLD BANK ECONOMIC REVIEW, VOL. 4, NO. 2

iWe %consilder a very-short-run equilibrium in which the size of the exportingindustry is fixed. Second, we consider the pressures at this equilibrium for theindustry to contract. When the size of the exporting industry is fixed, firmsrespond to the VER by reallocating sales away from the restricted to some other(unrestricted) export market. Such diversions of exports are assumed to haveincreasing opportunity costs, which implies that the commodities exported tothe two markets are not perfect substitutes in production-perhaps becausethey have different characteristics. Two effects of a VER are distinguished. First,the sales revenues of the exporting firms may rise or fall depending on theelasticities of demand in the restricted and unrestricted markets. Second, thereis a misallocation of resources. The VER moves the composition of the exportindustry's output to a point on the production possibilities curve where its slopeis no longer equal to the ratio of the two export prices; this constitutes alloca-tive inefficiency.

In the second step of our analysis, the industry is allowed to shrink inresponse to the VER. The VER reduces the marginal revenue products of theexporting industry's factors of production, and the industry will contract by anamount dependent on the elasticities of factor supply.

We proceed as follows. The impact of a VER on resource allocation inexporting countries is analyzed in section 1. In section II, we present an estimateof the effect of the U.S. Orderly Marketing Agreement (OMA) for nonrubberfootwear imports on the Korean leather footwear industry during the period1977 to 1981. A model is developed to estimate econometrically the slope ofthe production possibilities curve for the footwear industry. This helps todetermine the new point reached on the production possibilities curve as aconsequence of the OMA. The difference between the slope of the curve at thenew point and the new price ratio is used to estimate the fall in the marginalrevenue product for factors employed in the footwear industry. We find thatthe marginal revenue product may have fallen by as much as 9 percent becauseof the OMA. (The econometric techniques used in section II are described morefully in appendix A.) In section III we present the results of a simulationexercise. Combining our econometric estimates with alternative assumptionsabout output demand and factor supply elasticities gives illustrative estimatesof the likely welfare effects of the OMA. (The model used to derive the welfareeffects is described in appendix B.) Some concluding remarks are made insection IV.

I. REAL RESOURCE ALLOCATION IMPLICATIONS OF A VER

In this section, we present an analysis of the sales revenue effects and theresource allocation implications for an exporting country entering a VER. Wedemonstrate under fairly representative conditions that a VER will reduce themarginal revenue product of factor inputs in the affected industry, and hence

de Melo and Winters 211

reduce the size of the industry. To simplify the exposition, we assume that alloutput is produced by firms which are identical and perfectly competitive in allproduct and factor markets. The output is sold in one of two foreign markets.A VER restricts exports to one of these markets while those to the secondmarket remain unrestricted. In addition, while we assume that individual ex-porting firms are price takers in each export market, the industry as a wholefaces downward-sloping demand curves in each market.

The effects of a VER are presented in two steps. Initially it is assumed thatindustry size is fixed and that there are costs to diverting sales from the re-stricted toward the unrestricted market. With this assumption, it is a simplematter to analyze the revenue and distortionary implications of the VER. In thesecond step, we show that a VER will reduce the marginal revenue product offactors employed in the industry, which is likely to lead the industry to con-tract.

This two-step discussion of the effects of a VER is expositionally convenientand corresponds to the two-stage assumption about firm decisions adopted inthe econometric work of section II. We show in appendix B that the independ-ence of (weak separability between) input decisions and sales decisions is notfundamental for the results that are established here.

The assumption that there are increasing marginal costs to the diversion ofsales from the restricted toward the unrestricted market may be interpreted asindicating the short-run effects of a VER in an industry characterized by productdifferentiation. In the short run, where the quantities of factors employed inthe industry are fixed, a shift in production between outputs which use factorsin different proportions will result in increasing marginal costs. Moreover, ifone of the outputs has a specific factor which is in relatively inelastic supply-for example, a particular labor skill-the mere fact that the outputs are differ-entiated is sufficient to produce an increasing marginal rate of transformationbetween the two products.

The above assumptions allow us to represent our model diagramatically. Infigure 1, foreign export demands in the restricted (A) and unrestricted (B)markets are represented in quadrants I and II, respectively, while quadrant IIIdepicts the substitution possibilities facing the industry as it reallocates produc-tion between sales for market A and those for market B. It is obtained by theaggregation of the substitution possibilities facing each exporter. The bowed-out shape of the export transformation curve G(XA, XB) = X reflects the as-sumption of increasing costs of production associated with changing the prod-uct mix. Assuming fixed aggregate footwear production X, successive incre-ments in sales to market B impose increasing resource costs in terms of largerand larger decreases in export sales to market A. Quadrant IV is bisected bythe 450 line which translates export sales to A from quadrant III to quadrant I.

The unrestricted allocation, A*, is represented by the price-quantity pairs(PA, XA) and (P*, XB), where superscript asterisks are used to denote the

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unrestricted equilibrium. The slope of the export transformation curve is givenby

dXA GB<MTA B dXB GA

where Gi = aG/OX, > 0; i = A, B, indicate positive opportunity costs; andthe bowed-out transformation curve reflects the fact that opportunity costsincrease with output.'

The equilibrium for a competitive industry requires that

( 1 ) GA PA

and Pi = 0*Gi where 0* is the marginal cost of producing a unit of X:.In figure1, the equilibrium condition (equation 1) is represented by the tangency of theexport transformation curve and the price line, Pf, at the unrestricted equilib-rium, A*.

Now impose a VER which restricts exports to A to the level XA. The restrictedallocation is represented by the new price-quantity pairs (PA, XA) and (PB, 3XB)

where superscript bars indicate the restricted equilibrium. We decompose theeffects of the VER into two parts: a revenue effect, which reflects the way theVER affects the industry's revenue from exporting, and an allocative distortion,which arises as the economy is obliged to produce a non-optimal mix ofoutputs.

Consider the revenue effect. We have assumed that the industry as a wholecomprises a large number of atomistic firms and therefore cannot behave like adiscriminating monopolist. The presence of unappropriated monopoly rentsmeans that it is possible that the VER will raise industry revenues. Let EA and e"denote the elasticity of demand in the restricted and unrestricted markets,respectively, and assume CA, EB = 0. A departure from the free trade equilibriumwill raise revenues if marginal sales revenue is higher in B (unrestricted) than inA (restricted), that is, if P,(1 - 1 /EB) > PA(1 - i/EA). Thus if the elasticity ofdemand is much greater in the unrestricted than in the restricted market, a VER

may push sales allocation toward that which would be selected by a discrimi-nating monopolist.2

In the case described above, the VER has the same type of effect as anoptimum export tax. That exporting governments do not preempt the imposi-tion of an OMA by imposing export taxes of their own volition probably reflectstheir uncertainty about the long-run elasticities of demand they face, a fear of

1. Increasing marginal costs requires GAA, GBB > 0 and GAAGBB - GABŽ 0.2. While we do not wish to stress the empirical relevance of this possibility, it has been pointed out

in previous theoretical discussions of the effects of VERS in non-competitive markets. It is interesting tospeculate that the two-tier quota allocation system used in Korea (and elsewhere) implies that greatersales toward non-restricted markets may have the objective of revenue maximization. For furtheranalysis see Bark and de Melo (1988).


retaliation from importing governments, and a fear of reprimand from inter-national organizations. Of course, once importing governments have estab-lished OMAS, exporting governments are likely to try to exploit their potentialmarket power through alternative quota allocation schemes. Note that if theexporting industry had initially acted as a discriminating monopolist or facedoptimum export taxes, it would already have been maximizing its profits, andhence could only have suffered from the imposition of a VER.

Consider next the allocative distortions caused by the VER. Because we haveassumed at this stage that firms maximize revenue for a given level of X, whichis equivalent to maximizing profits, the new allocation must lie on the sameexport transformation curve as the old, and given the exogenous value of XA,the chosen point will be R. At this new equilibrium, the equality of relativeprices to the marginal rate of transformation no longer holds. The relative priceof A has been forced up by the constraint on sales so that it is tangent to thetranformation curve at A, but the marginal rate of transformation (MRTAB)has fallen to R as the relative output of A has fallen (see figure 1). Hence

GA GA> pA, whereas - < -

PB PB* GB G B

This violation entails a well-understood distortion cost, which is independentof whether total sales revenues have increased after the imposition of the VER.

For producers to choose point R voluntarily, they would have to face therelative price line (PAX'1B), which equals the marginal rate of transformation atR. PAv is known as the virtual price and, as is clear from figure 1, it implies arelative price less than both the unconstrained price (PA/PB) and the actualprice (PA/PB)

We now turn to the second step of the discussion and show that the VER willcreate an incentive for the industry to contract. With production and allocationdecisions separable, input mixes (which depend on factor prices) are indepen-dent of output mixes (which depend on output prices); hence, given fixedrelative factor prices, we can construct a composite factor, Z, with wage W.This allows us to characterize production in terms of the aggregate outputindex as X = X(Z) and, assuming constant returns to scale, we can select unitssuch that X Z. Hence we can assess the effects of a VER on the size of theindustry as measured by aggregate input Z.

In an unrestricted equilibrium, sales are allocated between markets in such away that the marginal revenue product of a factor devoted to producing goodsfor market A equals that of the factor if it were used to produce for market B.We may write the condition for an unconstrained equilibrium as follows:

dRA dRB dR(2)= =W

dZ dZ dZ

where RA is the revenue derived in market A, and so forth, W is the cost offactor Z and, in our earlier notation,


dR, p P X=

dZ G *i

To assess the effects of the VER on the size of the industry, we need toconsider whether the marginal revenue product of Z is increased or decreasedby the VER. This can be done entirely in terms of market B. Under free trade,the marginal revenue products are equal across markets, whereas under thebinding VER, only market B can accommodate marginal sales. The marginalrevenue product in B falls as more and more sales are switched to B, but whilethe VER is binding, the marginal revenue product in A is zero. Hence marginalproduct for a given Z falls. Constrained revenue maximization by the represen-tative firm implies that in the new equilibrium:

dRB PB(3) ~~~~~~dZ GB

Since the VER redirects sales from market A to market B, it drives up the costsof producing for market B (it reduces the marginal product of Z), because GBB

> 0. Thus, even if demand for B is perfectly elastic-that is, PB = PB-thevalue of the marginal product of Z is reduced by the VER. If demand is lessthan perfectly elastic, that is, PB < PB the effect is exacerbated by the drop inprice. Hence independent of whether the VER increases or decreases industryrevenue, it always reduces the marginal revenue product schedule of its factorinputs. Unless factor supply is entirely inelastic, a falling MRP schedule willcause the industry to reduce both its output and input levels.

The new long-term equilibrium could be represented in figure 1. The trans-formation curve shrinks inward and is tangential to a price ratio with slopebetween (P/IPB) and (P'/'PB) at a point with output (XA, X'A) where X'B >XB. Point N represents one possibility.

A more direct approach to analyzing the long run is directly in terms of themarket for the composite factor. Figure 2 illustrates three cases of interest. TheVER causes the marginal revenue product curve to fall, say from MRP' to MRP2.

In the very short run, in which factor inputs cannot be changed, the input levelremains at Zx, but there is a loss of factor rents and therefore welfare to factorowners equal to area AEFC. Thus there are no output losses but large distor-tion and resource costs. This, of course, is the implication derived by consid-ering the allocation part of the model alone. In the opposite case, if the foot-wear industry (in addition to each of its individual firms) faces an infinitelyelastic supply of Z, then the new input level is given by Z; there are largeoutput losses, but no distortionary resource costs because factors shift to otherindustries in which they are equally productive. Under these circumstances,0 = 0*, and the shift in the marginal revenue product curve is accommodatedby output contraction alone. In another case, the industry faces an upward-sloping supply curve for factors, the final input level is Z, which entails asmaller contraction but imposes welfare losses equal to the area AEDB. Now


Figure 2. Three Cases for the Market for the Composite Factor ZWhere the VER Causes the MRP Curve to Shift Down

Input price, W

W= W(Z)

A W = WB ----- -- MRP

C F

Z Z Z Aggregate input, Z

Note: Z*is the short-run case where Z is fixed at Z'. Z is the case where there is aninfinitely elastic supply of Z. Z is the case where there is an upward-sloping supply curvefor factors.

0 < 0*, and there is an efficiency loss, but it is smaller than that implied in thevery short run in which industry factor use is fixed.

In a more complete exposition of the implications of a VER, the number ofaffected markets would be increased and the two-step approach relaxed. Theempirical analysis in section II addresses the more general case in which salesare allocated to one restricted and two unrestricted markets, and we discussbelow how the analysis would be modified to increase the number of unres-tricted markets. As for the two-step approach, de Melo and Winters (1990)show for the general case of a two-output, one-input technology that spilloverto unrestricted markets and output contraction will occur unless there is a verystrong positive relation between output destined for one market and the costsof producing for others. (Their findings are also discussed briefly in appendixB.) Because marginal production costs for each market are likely to show onlysmall interdependencies, it is unlikely that the qualitative predictions of theabove analysis would differ in a more general setup.

Because we have only two markets, we have been able to establish thecontractionary effect of a VER by considering the marginal revenue product ineach market directly. With more markets, as in the empirical application be-low, it is more convenient to use an alternative approach, derived from Nearyand Roberts (1980). These authors show that a constrained equilibrium can beexpressed as an unconstrained equilibrium at a different set of prices. These


are the virtual prices, mentioned earlier, which are simply the set of prices atwhich, given the overall level of activity, actual quantities supplied in theconstrained equilibrium would be supplied voluntarily. For unconstrained mar-kets, virtual prices are equal to actual prices. Referring back to figure 1, thequantities given by R would be voluntarily supplied at the set of prices(PA', PB), whereas actual prices in the constrained case are represented by(PA, PB).

For any unconstrained equilibrium, the value of the marginal product arisingfrom an extra unit of aggregate input Z, optimally allocated, is a positivefunction of the set of prices (P1, . . ., Pj); where n - 1 is the number ofunrestricted markets. For a constrained equilibrium, the Neary-Roberts resultsallow us to calculate the value of the marginal product schedule by evaluatingthe same function at virtual prices (PV). The effect of a binding VER in marketA is to reduce PA below its actual price. Because, in unconstrained markets,actual and virtual prices are equal, the reduction in PA means that at least someprices fall and none rise and that therefore the value of the marginal productfalls. Although it is not possible, without knowledge of the factor supply curve,to determine equilibrium values for prices and output, this approach suggeststhat the VER puts downward pressure on output. This is the procedure used insection II to measure the shift in the marginal revenue product schedule; theequivalent of distance EF in figure 2.

II. ESTIMATING THE REDUCTION IN FACTOR DEMAND: KOREAN LEATHER

FOOTWEAR

In this section, we present estimates of the effect of the United States'sOrderly Marketing Agreement (OMA) on nonrubber footwear on the demandfor the factors employed in Korean leather footwear production. We use thesimple model described in the previous section: it is assumed that the Koreanfootwear industry produces an aggregate quantity of footwear using a singlecomposite factor of production, and subsequently allocates this aggregateamount to one of three markets according to a constant elasticity of transfor-mation (CET) allocation function. This simple function allows us to analyze,albeit indirectly, the efficiency implications of the OMA without access to spe-cific data on the allocation of factor inputs to sales in each market. The crucialparameter in our model is the elasticity of transformation, which is a measureof the extent to which production may be shifted between outputs destined fordifferent markets.

In terms of figure 1, it measures responsiveness to changes in the output mixalong a given export transformation curve. With this parameter value, it ispossible to predict the actual output mix in the omi period, and the differencebetween actual and virtual prices during the period. From the latter we cancalculate the extent of the shift in the marginal revenue product schedule forthe composite factor.


Using quarterly data for the period from the first quarter of 1975 (I) throughthe fourth quarter of 1986 (IV), we estimate the elasticity of transformationbetween supplies of leather footwear destined for three markets-the UnitedStates, the unconstrained European Community, (which comprises France, theFederal Republic of Germany, Italy, and the Netherlands), and the rest of theworld. The United States imposed the OMA on Korean exports of nonrubberfootwear between the third quarter of 1977 and the second quarter of 1981,inclusive (although the evidence suggests that the restrictions on Korea ceasedto be binding by mid-1980; Aw and Roberts 1986). Hence, the observationscorresponding to this period are not included in the estimation period. Theunconstrained European Community group, according to Hamilton (1989),imposed no quantitative restrictions on Korean footwear exports over oursample period. Some of the countries in the rest of the world did have importrestrictions on footwear, but they may reasonably be treated as unconstrainedoverall.

Following the model described in section 1, individual Korean exporters areassumed to be price takers. They seek to maximize revenues subject to a CET

transformation function, which relates the quantities of each type of exportfootwear to an overall index of output (input); that is,

max X piX, subject to [ i aiX' =XXi i i~

where Xi is exports to market i at price pi, X is the index of aggregate output,and y > 1.

Writing p = 1 / (-y - 1) for the elasticity of transformation, standard manip-ulation allows us to express the share of market i in total exports as (seeHickman and Lau 1973):

(4) si = ai(pi/p)P; i = 1, 2, 3

where si is the share of i in the volume of exports, si = Xi/E Xj,J

1/p

is a fixed-weight price index, and ai = ai-P.Although firms are price takers, the exporting industry is not, so the aggre-

gate Korean export price is potentially endogenous to our model. Both this factand the possibility of there being errors in variables suggest the need for morerobust methods of estimation than are possible for nonlinear systems of equa-tions with complex error structures. We decided, therefore, to linearize themodel about a base period (see Hickman and Lau 1973). If we set prices tounity in the base period (second quarter of 1984), introduce a time-trend with


value zero in the base period, and add seasonal factors and a lagged dependentvariable, we obtain

(5) Yit= p a, (Pi, - PI) + Nit + Y bikDk + X 1yit-i + u± ,k

where yi, -sia-a' is the deviation of i's share from its base value, ae%, ptI cxj Pj, is a base-weighted price index, t is a time trend incremented by one perquarter, E bikDk are seasonal effects for quarter k, k = 1, 3, 4 where thedummy for the second quarter has been suppressed because the base period isa second quarter, X1 represents dynamic effects on the share of market i of itsown lagged values, and u2t are stochastic errors.

Because yi, sums to zero over i in each time period, equation 5 for one of thethree markets must be dropped in estimation. We dropped the equation for theunconstrained European Community. We then estimated the remaining equa-tions by a procedure described in appendix A.

The final equation is given in table 1. The estimated elasticity of transfor-mation is perhaps a little low, given the anecdotal evidence that exists on thedegree of competition and product substitution-homogeneity in world footwearmarkets; but it is a fairly robust result. Moreover, two other pieces of evidencesuggest that Korean exports to different markets are imperfect substitutes. First,the unit values of Korean exports to different markets differ by up to 50

Table 1. The Allocation Function for Korean Leather Footwear ExportsVariable Estimated coefficient Standard error

p 1.311 0.756'YR -0.0013 0.0009'Y u 0.0024 0.00103R1 0.074 0.022'8UI -0.076 0.0213R3 0.060 0.019803 -0.063 0.0186R4 0.058 0.0198U4 -0.060 0.020X, 0.401 0.102r 0.137R2

Rest of the world 0.80United States 0.88Unconstrained European

Community 0.75Long-run elasticity of

transformations 2.19

Note: The subscript R refers to the rest of the world and the U to the United States; r is a first-stageestimate of the autocorrelation parameter.

a. Calculated as pl(1 - X,).Source: de Melo and Winters (1989, appendix).


Table 2. Estimated Effects of the OMA on Korean Leather Footwear Exportsto the United States, 1977-80

ProportionateActual minus difference between Change

predicted actual and virtual in aggregateshare price price index

Year and quarter (1) (2) (3)

1977,3 -0.176 -0.121 -0.0951977,4 -0.024 -0.017 -0.0131978,1 -0.076 -0.050 -0.0391978,2 -0.159 -0.103 -0.0811978,3 -0.098 -0.056 -0.0441978,4 -0.093 -0.051 -0.0401979,1 -0.208 -0.096 -0.0761979,2 -0.188 -0.081 -0.0631979,3 -0.284 -0.110 -0.0871979,4 -0.159 -0.065 -0.0511980,1 -0.052 -0.023 -0.0181980,2 -0.092 -0.040 -0.031

Source: table 1 and authors' calculations.

percent, which suggests that there may indeed be genuine product heterogene-ity. Second, the estimates in table 1 display dramatically different seasonalpatterns-with the allocation of shares between the United States and the restof the world switching by over 10 percentage points with the season.

Table 2 explores the effects of the OMA on Korean exports to the UnitedStates more closely. On the basis of our estimates, we can predict the share ofexports to the United States in the OMA period if quantities had been uncon-strained at the actual price. Column 1 reports the difference between the actualand predicted shares during the OMA period. It is consistently negative, whichsuggests that the OMA was binding, although it shows signs of weakening during1980. Column 2 approximates the proportionate difference between the virtualand actual prices of exports to the United States. Because the actual U.S. sharefalls short of that predicted by the export allocation model, the virtual pricefor the United States is below the actual price by as much as 12 percent (inthird quarter of 1977). Thus the OMA may be seen to have had an effectequivalent to reducing the price of exports to the United States by 5-12 percentbelow actual levels with no compensating price rises in other markets. Thismakes it clear that the OMA put pressure on the Korean footwear industry tocontract.

The extent of the contractionary pressure can be calculated as the differencein the aggregate price index evaluated at actual and virtual prices. This calcu-lation, reported in column 3 of table 2, is a linear approximation to the changein the marginal return to the aggregate factor in the leather footwear sector. Itshows that the marginal revenue product of the factors of production in the


Figure 3. Index of Employment and Output in Footwear Relative to AllManufacturing (1980 = 1)

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0.41974 1975 1976 1977 1978 1979 1980 1981 19'82 19'83

leather footwear industry declined by as much as 9 percent because of theOMA. 3

The econometric estimates strongly suggest that the Korean footwear indus-try would have contracted during the period of the OMA. This prediction issupported by time series data on output, employment, and wages of the Koreanfootwear sector. These data are illustrated in figure 3, which reports footwearoutput and employment relative to the corresponding series for the entiremanufacturing sector: although Korean industry generally contracted over thisperiod (see appendix table A-i), the footwear sector suffered more than aver-age. Output and employment in the footwear industry peaked in 1978, oneyear after the signing of the OMA agreement. This peak is later than predictedby our model, but it is not out of line with the detailed account of the OMAgiven by Yoffie (1983). He remarks that Korean producers went to considerablelengths to negotiate the OMA in a fashion that allowed extended periods ofadjustment. Thus it is quite conceivable that output and employment remainedhigh into 1978.

3. Comparisons with free trade rather than actual prices would reduce these estimates somewhat. Inthe absence of an estimated elasticity of demand, however, the former are not calculable, but the higherthe elasticity of demand the smaller the difference. In our simulation results below, we use free tradeprices.


One of the causes of the Korean slump was rising real wages over the period1977-79, which might have harmed labor-intensive industries such as foot-wear. In fact, wages in footwear fell during 1978 relative to those in otherlabor-intensive sectors such as textiles, apparel, and leather products. Thusalthough it cannot be entirely ruled out that the time series on footwear reflectonly economywide phenomena, there is some evidence of particular hardshipin the footwear sector. Certainly we find nothing to refute our prediction thatthe OMA caused a contraction of Korea's footwear sector.

III. ILLUSTRATIVE WELFARE CALCULATIONS

The results above confirm our hypothesis that a VER leads to output contrac-tion and has adverse effects on efficiency if the factors employed in the industryare not available to it in perfectly elastic supply. However, as discussed insection I, a VER also results in revenue effects which may either reinforce orcounteract the efficiency costs. (It was demonstrated in section I that the latter,in the long run, lead the industry to contract and to reduce factor incomes.)The combined long-run effect is captured in the calculation of the welfareeffect, which is estimated by simulation techniques in this section. Welfareeffects are calculated by adding the gains in or losses of profits to firms and theloss of income to factors.

The simulation model is used to provide rough orders of magnitude of thepotential welfare effects of a VER, using the U.S. OMA on Korean exports ofleather footwear as a reference case. The calibrated simulations are basedgenerally on the model presented in section 1, with constant foreign priceelasticities of demand; a CET function describing sales allocation; and a con-stant elasticity of factor supply. (Further details are given in appendix B.)

For the reference-case calculations, we use our estimate of the elasticity oftransformation from section 11 to measure the ease with which exporters maydivert sales from restricted to unrestricted markets and complement it withrough estimates of factor supply elasticities and price elasticities of exportdemand. Our estimates of the price elasticity of export demand are consistentwith the range of 0.5-1.0 reported by Pearson (1983, p. 78) and Goldstein andKhan (1985).

Welfare is measured by the sum of profits and factor incomes, and the changein welfare is expressed as a proportion of variable factor (Z) income before theVER. The change in factor demand from the restricted industry affects the wagesthroughout the markets in which the factors are traded and the contraction ofthe restricted industry drives down factor rewards both for itself and for anyother industry using the same factors. Hence a given wage reduction has alarger impact on welfare, the larger the stock of factors affected. This effect isrepresented crudely in the welfare calculations by L, the size of the total factorstock affected relative to the initial size of the affected industry, Z. A value ofL = 1 implies that initially only the VER-affected industry employs the factor


concerned; a value of 5 implies that the VER industry originally employed 20percent of the relevant factor stock. Because L will vary depending on theindustry under consideration, we give calculations for cases where the marketfor the variable factor Z is 1, 5, or 10 times the initial allocation to the industryunder the VER.

Illustrative calculations for a range of elasticities are given in table 3. For all

calculations, it is assumed that there is a 10 percent reduction in the volume of

sales to the restricted market, where the initial share of exports to the restricted

market is 42 percent of total exports (a figure corresponding to the leather

footwear case). Before examining the results for the different elasticities shown

as the five cases of the table, in which several elasticities are varied simultane-

ously, we describe briefly the effects of varying elasticities one by one and

compare the results with those in case 1, where all elasticities are unity.

In the case of unitary export demand elasticities, there are no sales revenue

effects, so it is easy to isolate the effects of varying supply elasticities. The more

difficult it is to reallocate the existing volume of production, the higher the

Table 3. Illustrative Welfare CalculationsCase

Item 1 2 3 4 5

Value of elasticity

Type of elasticityPrice elasticity of restricted demand, cA 1.0 0.3 0.5 1.0 2.0Price elasticity of unrestricted demand, eB 1.0 0.6 1.0 2.0 4.0Elasticity of transformation, p 1.0 0.5 1.5 1.5 3.0Elasticity of factor supply, e- 1.0 0.5 2.0 2.0 3.0

Result of simulationVariableOutputb -5.0 -3.9 -4.3 -4.5 -4.1Sales revenueb 0.0 11.6 4.6 0.0 -2.1Factor wageb -4.0 -7.7 -2.2 -2.3 -1.4Welfarec

1 6.2 19.7 10.2 5.5 2.75 -0.5 6.9 6.5 1.7 0.410 -8.9 -9.1 1.9 -3.0 -2.5

Note: Notation is given in appendix B, equation, B-2. Unrestricted equilibrium: XA = 100; XB140; P = 1.00; Z = 100.

a. Size of market for Z in relation to initial allocation of Z in industry subject to VER.b. Percentage change.c. Change in income expressed as a share of initial variable factor income (see appendix B, equation

B-13). These changes are shown for three values of the size of the total factor stock affected relative tothe initial size of the affected industry.

Source: table 1 and authors' calculations.


efficiency cost of a given VER because the adjustment comes from outputcontraction rather than from sales reallocation. Likewise, as explained in sec-tion I, the higher the elasticity of factor supply, the lower the efficiency costsof a VER. Indeed, a similar variation (around unity) of the elasticity of factorsupply has more of an effect on efficiency than will an equal variation of theelasticity of transformation.

Cases 2 through 5 give estimates of the welfare effects of a VER for low,medium, and high sets of elasticities. The results in case 4 may be viewed asbest guess calculations. In the case of a VER, there is a net loss if the market forZ is large. But if the market for Z is small (relative to the initial allocation ofZ to the industry), there is a net gain from the VER despite the negativeefficiency effects because of their relatively smaller weight in the welfare calcu-lation. The same is true for the case where all the elasticities are low (case 2).The larger efficiency costs are offset by the larger revenue gains. It is alsonoteworthy that the simulated decreases in the marginal revenue product of Z(represented by the factor wage row of table 3) are similar in magnitude to therange reported from the econometric estimates in column 3 of table 2. Finally,in case 5, with higher demand elasticities, the revenue effect becomes negative,which implies larger welfare losses. Thus, if demand elasticities are not too lowand supply elasticities are not too high, a VER is likely to lead to a welfareloss.4

Although the net effects of the VER are fairly small in table 3, the gross effectsare significant. The VER increases profits for those with the right to export tothe restricted markets but harms all other agents. In particular, labor is likelyto lose from industrial-country protection, an ironic result in light of the factthat protection is often advocated as a means of protecting workers. If so,protection should be seen as a means of protecting rich industrial countryworkers at the expense of workers in poor developing countries.

IV. CONCLUSIONS

This article has presented a simple model to analyze the revenue and effi-ciency effects of a VER at the industry level. Motivated by the evidence thatdeveloping countries often have limited success in switching sales toward unres-tricted markets, we have analyzed the impact on the exporting industry. Inorder to do this, we have separated revenue effects arising from sales realloca-tion toward unrestricted markets from efficiency effects arising from outputcontraction.

The analytical discussion of the effects of a VER was then corroborated withan application to the U.S. OMA agreement with Korean exporters of leather

4. The elasticity of factor supply (E,) is not independent of the relative size of the industry in thefactor market (L). For example, for an industry like footwear, f5 is likely to be in the range of 2-4 andL perhaps 10 or more, whereas in textiles, the corresponding pair would be e, in the range of 0.5-2.0and L around 5.


footwear. The econometric estimates indicate both a limited ability to switchsales toward unrestricted markets and a sharp fall in the marginal revenueproduct of factors employed in the Korean leather footwear industry during theperiod where the OMA was in effect. Combined with extraneous estimates ofexport demand and factor supply elasticities, illustrative welfare calculationssuggest that the OMA may well have resulted in a welfare loss to exportingcountries, especially if demand elasticities are relatively elastic and supply re-sponses relatively inelastic.

APPENDIX A

This appendix presents a detailed description of the econometric model ofexport allocation introduced in section II and an account of its estimation. Weassume that exporters are price takers and that they seek to maximize theirrevenues subject to a CET transformation function relating the quantities ofeach type of footwear export to an overall index of output (input). Theirobjective is

(A-1) max E piX1 subject to [atxij = XXi i

where Xi is exports to market i, at price pi, X is the index of aggregate output,and 7> 1.

Standard manipulations (see Armington 1969) produce supply functions forthe individual markets,

(A-2) Xi = ar-P(pi/p*)PX

where p* is the dual CET price index of X given by:

(A-3) * = k a5p(+PJ11+p)

and

P L1- 1]is the (negative of the) elasticity of transformation between exports for any pairof markets; p > 0.

Further manipulation (see Hickman and Lau 1973) transforms equation A-2into the more convenient form:

Xi = c'ip4 ajpj1 x

or

(A-4) Si= ai(pi/p)p + u,


where X _ E X. is a simple aggregation of exports, s, is the share of i in thevolume of exports,

P [E arPt]

is a fixed-weight price index, (xi = a,-", and ui is a stochastic component addedat this stage for estimation purposes.

To facilitate the treatment of simultaneity and errors in variables, equationA-4 is linearized about a base period. We used the second quarter of 1984 asthe base because it lay well outside the period of possible rationing, and yetwas relatively central to our sample of unrationed observations. Subsequenttests suggested that the choice of base period affects the results slightly, but notsufficiently to disturb the qualitative conclusions in the text. If we set prices tounity in the base period, introduce a time trend with value zero in the base,and add seasonal factors and dynamics, the linearization gives

(A-5) yi, P <(pit - Pt) + Tit + E bi,kD + X,Yit-, + X4Yit-4 + Uit

where Yit- si - ae' is the deviation of i's share from its base value,a% p,Pt ao,p. is a base-weighted price index, t is a time trend incrementedby one per quarter, bi(Dk are seasonal effects for quarter k, k = 1, 3, 4 where

k i the dummy for quarter two has been suppressed because the base period is asecond quarter, and Xl, X4 represent dynamic effects on the share of market i,felt through lags of itself.

Adding up requires that z a. = 1 and that L (5k = 0 eY = S uj, = O for allk and t. The first condition is satisfied automatically; the latter, by droppingthe equation for the unconstrained European Community. Usually with thisprocedure, the final estimates are invariant with respect to the equationdropped, but because of the methods required by the errors in the variables,that is the use of instrumental variables, this is not so. In practice, however,the choice made very little difference.

Adding up also requires that, unless the errors are characterized by full vectorautoregression, the dynamic structure implied by the lags X, and X4 must becommon to all commodities. The lag X therefore appears in both equations asa cross-equation restriction. The use of lagged dependent variables may bejustified on several grounds-for example, partial adjustment of price expecta-tions, as in Hickman and Lau (1973), or habit formation. For systems of sum-constrained equations, it represents by far the most convenient approach todynamic generalization. The choice of lags 1 and 4 to capture the dynamicswas made a priori on the basis of previous experience with quarterly data sets.

Equation A-5 may be stacked over i and written in matrix form:


F ~~~~~~~~~~~~~~~~~~~~11_I _ c4(P 1 -p) t O D O D3 0D4O0Ly, L4y1 _. r ui(A-6) I 1~2 +

Y2 0120(P2 -P) 0 tO0 D1 0 D, 0 D, Ly, L'y, 621 L 2614

624

L 4

where L is the lag operator and all the roman letters denote (n x 1) vectors,where n is the number of observations.

Ignoring the errors in variables, equation A-6 may be simply estimated allow-ing for autocorrelation and cross-equation correlations. Following Parks (1967),we first estimate A-5 for each commodity separately, and calculate a singlefirst-order autocorrelation coefficient. (The serial correlation adjustment factormust be common to all equations if the system is to add up). Transforming thedata appropriately, we then reestimate by commodity to calculate E(iiuj),where the iu are the errors from the transformed equations. Finally, using thesevariances and covariances, we transform the data again to estimate equationA-6 by generalized least squares.

To allow for the simultaneity and the errors in variables, we use instrumentalvariable estimation. The technique presumes that the instrumental variables arecorrelated with the true values of the variables in equation A-5 but not theirerrors of observation. If this is true, our estimates are consistent and asymptot-ically efficient. Instruments were drawn from both the importing countries(industrial production, the wholesale price index for manufactures, and theexchange rate vis-a-vis the dollar) in order to reflect demand factors, and fromKorea (the per unit value of manufactured exports, the index of industrialproduction, and the dollar exchange rate) to reflect broad supply-side phenom-ena. Whenever Ly and L' are included in the equation, the instrumental varia-bles are also included in lagged form. Finally, the genuinely exogenous varia-bles in A-6-that is, D, and t-are also included in the set of instruments.

The estimation method is based on Aigner and others (1984). We assumethat there exists a true relation equivalent to equation A-6 but without errorsin variables, and which may be written as:

(A-7) y = V + u

where t represents the true value of X and y and u have their usual definitions.The relation between the true t and the observed X independent data is

(A-8) X + V


There also exists a set of relations between the k true independent variablesand the I indicator (instrumental) variables (Z).

(A-9) Z = 4r' + A.

The error terms V and A are assumed to be independently normally distributedwith zero means and also to be independent of t. The covariances of the rowsof V and A (v, and a) are given by Q and 0 respectively and the variance of uby a2 . The true independent variables are assumed to have an expected scaledcross-product matrix, K = Em-'t't, where m = 2n is the number of rows inthe matrixes y, X, Z, (, V, and A. Following Aigner and others, we can writethe various covariance matrices E= Em'I'7, for I, J = X, y, Z as

(A-lOa) =yy a2 + f3'Kf3

(A-lOb) Exy= K)3

(A-10c) X= rK/3

(A-lOd) ZZ= K + Q

(A-1Oe) 1zx = rK

(A-lOf) EZZ = rKr' + 0Equations (A-10c) and (A-IOe) yield

Ezy = ZZX

from which, multiplying both sides by EzxEz- and substituting sample valuesS 1 for population values E we obtain

(A-11) 13 = (zszx)-'s'xs~Z'S'Y[X' Z (Z' Z)-')X' Z] (Z' Z)-' Z'y.

B is multivariately normally distributed with asymptotic variance

(A-12) var ( a') = (cr2 + 1' 00) (SzxS' S)-'

which is the minimum variance bound that can be derived by linear methods.We approximate A-12 below by substituting l8 for , and using A-10 to expressthe first bracket in terms of observables.

System A-10 presumes that the errors are independently and identically dis-tributed, but in our case we need to allow for the presence of autocorrelationand the fact that E(u1tu2 ,) * 0 where ul and u2 are subvectors of u referring tothe first and second equations. In fact, however, these modifications makevirtually no difference to the estimator. Taking the latter first, partitioning allvariables in A-7 to A-9 conformably with u, and u2, versions of A-10 may be


derived for all combinations of yi, Xi and Z7, i = 1, 2. If the only change inassumption is that E(uiuj) = atj, i F4 j, only A-lOa is changed; it becomes

(A-lOa') ZYY, = e, + ,'KO

In all other equations, the partitioned covariances are the same as the unparti-tioned ones in A-10. This means that the same instrumental estimation methodmay be applied to a set of first-stage estimators to derive the a , which are thenused to transform all the observable data into the form assumed in the mainstage just described. Provided that the estimates of a.j are consistent, the asymp-totic properties of the final estimates are unchanged. A similar approach istaken to the autocorrelation.

The variance estimate (equation A-12) may be used to conduct statisticalinference on the coefficients. The validity of a set of q linear constraints, Qf,r, may be explored by means of the test statistic

(Q3 - r)' [Q Var (f)Q' I-' (Q3 - r)

which is distributed x2 under the null hypothesis (see Amemiya 1985). Thistest suggested that it was acceptable to set X4 = 0 in the final equation.

(The data were collected and prepared by Taeho Bark and Paul Brenton fromKorean Customs data publications. They are fully described in the appendix ofde Melo and Winters 1989. In terms of the final classifications in table 2 ofthat source, leather footwear is defined here as headings 6402.1000-6402.4900.)

Appendix Table A-1. The Korean Footwear Sector, 1974-83Footwear as a percentage of total

Footwear manufacturingYear Employment' Output" Wages' Employment OUtpUtd Wages

1974 6,600 33 303 0.518 85.3 85.31975 11,000 53 364 0.788 114.5 77.91976 14,200 74 493 0.84 121.3 82.61977 19,800 108 657 1.046 147.1 85.11978 26,000 159 846 1.249 174.9 79.31979 22,000 107 1,136 1.055 105.0 81.11980 22,700 100 1,366 1.127 100.0 79.21981 26,000 111 1,538 1.293 97.9 74.81982 36,500 113 1,809 1.77 94.6 78.41983 40,500 122 2,025 1.86 87.8 80.2

a. Person-years.b. Index: 1980 = 100.c. In thousands of won per year.d. Ratio of index numbers: 1980 = 100.Source: U.N. Industrial Development Organization data.


APPENDIX B

General Model and Welfare Calculations

General model. Consider the general case of firms in perfect competition inwhich the allocation and input decisions are made jointly.5 In this case, weakseparability is not imposed on the allocation and production decisions. Tech-nology is represented by a one-input, two-output production function. Letvariable factor requirements, Z, allocated to the restricted (XA) and unrestricted(XB) markets be given by:

(B-1) Z = G(XA, XB)

where Z is the quantity used of the composite factor, Gi is aZiaX, > 0, and Gis homothetic and homogeneous of degree r < 1. Under the assumption ofprofit maximization, de Melo and Winters (1990) show that the imposition ofa VER on sales to A(XA < X*), leads to the following expressions for output(B-2) and for national welfare (B-3).

(B-2) =AH [B GB Ge

[XB eL G ZeG]

(B-3) dXA LLEA EB_ B N] G]

where eA, eB, eN < 0 are respectively the elasticities of demand for A, B, andthe variable factor Z with respect to the wage in other sectors using Z, e2 > 0is the elasticity of supply of Z. From B-2, it is clear that a VER in A will mostlikely lead the industry to contract if one assumes increasing marginal costs,that is, Gii > 0, and if one recognizes the constraints imposed by the second-order conditions for profit maximization. Only very strong (and implausible)interactions between A and B leading to a large positive value for GAB wouldlead the industry to expand. Hence, a VER is likely to lead the industry tocontract.

From B-3, the change in national welfare defined as the sum of industryprofits and factor payments is determined by an allocation component whichmeasures whether switching sales from A to B raises revenue, and a size com-ponent which measures whether switching factors across sectors is beneficial.

Welfare calculations. The welfare calculations in section III come from anumerical application of the model presented in section I, with constant elastic-ity of demand curves (equations B-4 and B-5); a CET function to allocate salesbetween the restricted and unrestricted markets A and B (equation B-6); and a

5. This appendix draws on de Melo and Winters (1990).


constant elasticity of supply function for the factor, Z (equation B-11). Anunrestricted equilibrium is described by the following set of equations:

(B-4) XA = AA PEA CAA > °

(B-5) XB =AB PB eB > 0

(B-6) = AC(oAXA + aBXB) p P = 1/Y-1; eY > 0

(B-7) PA =*A ) AC CA(XA/X)"'

(B-8) PB = AC l B(XB/X)1P

(B-9) X = XS

(B-10) XS = ASZeZ

(B-1l1) Z = Az PEz;,Ez > O

(B-12) Pz = Aso*

where Ai, (i c A, B, C, Z, S) are normalizing constants determined by calibra-tion, that is, constants calculated so that the set of equations describing themodel is satisfied for the initial levels of prices and quantities. In the free-tradeequilibrium, industry profits, 7r, are zero as sales revenue equals payments toZ, PzZ

With the VER, XA is fixed at XA < XA and the first-order condition for theallocation to the restricted market (B-7) is dropped. As explained in section I,as a result of the VER, 0 > 0* (unless ez = oo).

The welfare measure is:

(B-13) AW = W, - W* = (Air + APZL)/PZ

where L is a scalar indicating the size of the industry in the market for Z.The calculations in section III are obtained by solving the model represented

by equations B-4 to B-12 for an unrestricted equilibrium and for a restrictedequilibrium with XA = 0.9 X*. When elasticities are varied, the Ai parametersare recalibrated so as to start from the same initial unrestricted values for pricesand quantities.

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